It is common for AG pool packages to come with mismatched pump/filter combos. I have asked Ben to offer a recommendation for you in regards to your equipment.

That is a cartridge filter.

Regarding the chemical kit -- even if you do get it, I would advise not using it until you tell us exact ingredients and letting someone here help you decide if it is ok to use or not. Many pool store chemicals are what we call voodoo mixes and often have ingredients in them that you do not want in your pool.